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Hubbard–Stratonovich transformation

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396: 236: 267:. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field. The procedure is widely used in 80: 287:. A major difficulty arising in the simulation with such field theories is their highly oscillatory nature in case of strong interactions, which leads to the well-known 265: 291:. The problem originates from the repulsive part of the interaction potential, which implicates the introduction of the complex factor via the HS transformation. 17: 231:{\displaystyle \exp \left\{-{\frac {a}{2}}x^{2}\right\}={\sqrt {\frac {1}{2\pi a}}}\;\int _{-\infty }^{\infty }\exp \left\,dy,} 437: 411: 466: 456: 283:
The resulting field theories are well-suited for the application of effective approximation techniques, like the
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Stratonovich, R.L. (1958). "On a Method of Calculating Quantum Distribution Functions".
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Hubbard, J. (1959). "Calculation of Partition Functions".
310:Об одном методе вычисления квантовых функций распределения 278: 247: 83: 259: 230: 448: 431: 323: 307: 438: 424: 146: 74:. It is defined via the integral identity 218: 66:in the many-body interaction term of the 352: 279:Calculation of resulting field theories 14: 449: 50:and popularized by British physicist 390: 275:, and electronic structure theory. 24: 18:Hubbard-Stratonovich transformation 160: 155: 25: 478: 394: 346: 301: 271:, classical particle physics, 46:invented by Russian physicist 13: 1: 294: 410:. You can help Knowledge by 308:Стратонович, Р. Л. (1957). 7: 10: 483: 389: 54:. It is used to convert a 404:condensed matter physics 377:10.1103/PhysRevLett.3.77 309: 285:mean field approximation 241:where the real constant 356:Physical Review Letters 322:Translation available: 467:Condensed matter stubs 457:Functions and mappings 406:-related article is a 327:Soviet Physics Doklady 289:numerical sign problem 261: 260:{\displaystyle a>0} 232: 72:auxiliary scalar field 48:Ruslan L. Stratonovich 262: 233: 245: 81: 58:into its respective 29:Hubbard–Stratonovich 369:1959PhRvL...3...77H 340:1957SPhD....2..416S 164: 70:and introducing an 62:by linearizing the 257: 228: 147: 419: 418: 273:spin glass theory 199: 144: 143: 106: 16:(Redirected from 474: 440: 433: 426: 398: 391: 381: 380: 350: 344: 343: 321: 305: 266: 264: 263: 258: 237: 235: 234: 229: 217: 213: 200: 198: 190: 189: 180: 163: 158: 145: 142: 128: 127: 122: 118: 117: 116: 107: 99: 64:density operator 21: 482: 481: 477: 476: 475: 473: 472: 471: 447: 446: 445: 444: 387: 385: 384: 351: 347: 320:(6): 1097–1100. 314:Доклады АН СССР 311: 306: 302: 297: 281: 269:polymer physics 246: 243: 242: 191: 185: 181: 179: 175: 171: 159: 151: 132: 126: 112: 108: 98: 94: 90: 82: 79: 78: 56:particle theory 23: 22: 15: 12: 11: 5: 480: 470: 469: 464: 459: 443: 442: 435: 428: 420: 417: 416: 399: 383: 382: 345: 316:(in Russian). 299: 298: 296: 293: 280: 277: 256: 253: 250: 239: 238: 227: 224: 221: 216: 212: 209: 206: 203: 197: 194: 188: 184: 178: 174: 170: 167: 162: 157: 154: 150: 141: 138: 135: 131: 125: 121: 115: 111: 105: 102: 97: 93: 89: 86: 44:transformation 37:transformation 9: 6: 4: 3: 2: 479: 468: 465: 463: 460: 458: 455: 454: 452: 441: 436: 434: 429: 427: 422: 421: 415: 413: 409: 405: 400: 397: 393: 392: 388: 378: 374: 370: 366: 362: 358: 357: 349: 341: 337: 333: 329: 328: 319: 315: 304: 300: 292: 290: 286: 276: 274: 270: 254: 251: 248: 225: 222: 219: 214: 210: 207: 204: 201: 195: 192: 186: 182: 176: 172: 168: 165: 152: 148: 139: 136: 133: 129: 123: 119: 113: 109: 103: 100: 95: 91: 87: 84: 77: 76: 75: 73: 69: 65: 61: 57: 53: 49: 45: 42: 38: 34: 30: 19: 412:expanding it 401: 386: 360: 354: 348: 331: 325: 317: 313: 303: 282: 240: 60:field theory 52:John Hubbard 41:mathematical 39:is an exact 36: 32: 28: 26: 68:Hamiltonian 462:Transforms 451:Categories 295:References 363:(2): 77. 202:− 177:− 169:⁡ 161:∞ 156:∞ 153:− 149:∫ 137:π 96:− 88:⁡ 365:Bibcode 336:Bibcode 334:: 416. 402:This 408:stub 252:> 27:The 373:doi 318:115 166:exp 85:exp 453:: 371:. 359:. 330:. 312:. 35:) 33:HS 439:e 432:t 425:v 414:. 379:. 375:: 367:: 361:3 342:. 338:: 332:2 255:0 249:a 226:, 223:y 220:d 215:] 211:y 208:x 205:i 196:a 193:2 187:2 183:y 173:[ 140:a 134:2 130:1 124:= 120:} 114:2 110:x 104:2 101:a 92:{ 31:( 20:)

Index

Hubbard-Stratonovich transformation
mathematical
transformation
Ruslan L. Stratonovich
John Hubbard
particle theory
field theory
density operator
Hamiltonian
auxiliary scalar field
polymer physics
spin glass theory
mean field approximation
numerical sign problem
Soviet Physics Doklady
Bibcode
1957SPhD....2..416S
Physical Review Letters
Bibcode
1959PhRvL...3...77H
doi
10.1103/PhysRevLett.3.77
Stub icon
condensed matter physics
stub
expanding it
v
t
e
Categories

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